# Coverage for pygeodesy/points.py : 95%

## 499 statements 473 run 26 missing 43 excluded

Hot-keys on this page

r m x p toggle line displays

j k next/prev highlighted chunk

0 (zero) top of page

1 (one) first highlighted chunk

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 | # -*- coding: utf-8 -*- u'''Functions to handle collections and sequences of C{LatLon} points specified as 2-d U{NumPy<https://www.NumPy.org>}, C{arrays} or tuples as C{LatLon} or as C{pseudo-x/-y} pairs. C{NumPy} arrays are assumed to contain rows of points with a lat-, a longitude -and possibly other- values in different columns. While iterating over the array rows, create an instance of a given C{LatLon} class "on-the-fly" for each row with the row's lat- and longitude. The original C{NumPy} array is read-accessed only and never duplicated, except to create a I{subset} of the original array. For example, to process a C{NumPy} array, wrap the array by instantiating class L{Numpy2LatLon} and specifying the column index for the lat- and longitude in each row. Then, pass the L{Numpy2LatLon} instance to any L{pygeodesy} function or method accepting a I{points} argument. Similarly, class L{Tuple2LatLon} is used to instantiate a C{LatLon} for each 2+tuple in a list, tuple or sequence of such 2+tuples from the index for the lat- and longitude index in each 2+tuple. @newfield example: Example, Examples ''' from pygeodesy.basics import EPS, isint, issequence, map1, PI_2, \ property_doc_, property_RO, R_M, _Sequence, \ _xcopy, _xinstanceof, _xkwds # PYCHOK indent from pygeodesy.dms import F_D, latDMS, lonDMS, parseDMS2 from pygeodesy.errors import CrossError, crosserrors, _incompatible, \ _IndexError, _IsnotError, _TypeError, \ _ValueError, _xkwds_pop from pygeodesy.fmath import favg, fdot, Fsum, fsum from pygeodesy.formy import equirectangular_, latlon2n_xyz, points2 from pygeodesy.interns import _COMMA_SPACE_, _datum_, _height_, _item_ps, \ _item_sq, _lat_, _lon_, _name_, NN, _other_, \ _point_, _UNDERSCORE_, _valid_, _x_, _y_ from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY from pygeodesy.named import Bounds2Tuple, Bounds4Tuple, _callname, classname, \ LatLon2Tuple, _NamedTuple, NearestOn3Tuple, nameof, \ notImplemented, notOverloaded, PhiLam2Tuple, \ Vector4Tuple, _xnamed from pygeodesy.nvectorBase import NvectorBase, _N_vector_ from pygeodesy.streprs import hstr, instr, pairs from pygeodesy.units import Radius, Scalar_ from pygeodesy.utily import degrees90, degrees180, degrees360, degrees2m, \ unroll180, unrollPI, wrap90, wrap180 from inspect import isclass from math import atan2, cos, fmod, hypot, radians, sin __all__ = _ALL_LAZY.points __version__ = '20.07.24' class LatLon_(object): # XXX imported by heights._HeightBase.height '''Low-overhead C{LatLon} class for L{Numpy2LatLon} and L{Tuple2LatLon}. ''' # __slots__ efficiency is voided if the __slots__ class attribute # is used in a subclass of a class with the traditional __dict__, # see <https://docs.Python.org/2/reference/datamodel.html#slots> # and __slots__ must be repeated in sub-classes, see "Problems # with __slots__" in Luciano Ramalho, "Fluent Python", page # 276+, O'Reilly, 2016, also at <https://Books.Google.ie/ # books?id=bIZHCgAAQBAJ&lpg=PP1&dq=fluent%20python&pg= # PT364#v=onepage&q=“Problems%20with%20__slots__”&f=false> __slots__ = (_lat_, _lon_, _name_, _height_, _datum_) def __init__(self, lat, lon, name=NN, height=0, datum=None): '''Creat a new, mininal, low-overhead L{LatLon_} instance, without heigth and datum. @arg lat: Latitude (C{degrees}). @arg lon: Longitude (C{degrees}). @kwarg name: Optional name (C{str}). @kwarg height: Optional height (C{float} or C{int}). @kwarg datum: Optional datum (C{Datum}) or C{None}. @note: The lat- and longitude are taken as-given, un-clipped and un-validated . ''' try: # most common use case self.lat, self.lon = float(lat), float(lon) except (TypeError, ValueError): self.lat, self.lon = parseDMS2(lat, lon, clipLat=0, clipLon=0) # PYCHOK LatLon2Tuple self.name = str(name) self.height = height self.datum = datum def __eq__(self, other): return isinstance(other, LatLon_) and \ other.lat == self.lat and \ other.lon == self.lon def __ne__(self, other): return not self.__eq__(other) def __repr__(self): return self.toRepr() def __str__(self): return self.toStr() def classof(self, *args, **kwds): '''Instantiate this very class. @arg args: Optional, positional arguments. @kwarg kwds: Optional, keyword arguments. @return: New instance (C{self.__class__}). ''' if 'name' in kwds: return self.__class__(*args, **kwds) else: return self.__class__(name=self.name, *args, **kwds) def copy(self, deep=False): '''Make a shallow or deep copy of this instance. @kwarg deep: If C{True} make a deep, otherwise a shallow copy (C{bool}). @return: The copy (C{This class} or subclass thereof). ''' return _xcopy(self, deep=deep) def heightStr(self, prec=-2): '''Return a string for the height B{C{height}}. @kwarg prec: Optional number of decimals, unstripped (C{int}). @see: Function L{hstr}. ''' return hstr(self.height, prec=prec) @property_RO def latlon(self): '''Get the lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return LatLon2Tuple(self.lat, self.lon) @property_RO def latlonheight(self): '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.height) @property_RO def _N_vector(self): '''(INTERNAL) Get the minimal, low-overhead (C{nvectorBase._N_vector_}) ''' return _N_vector_(*latlon2n_xyz(self.lat, self.lon), h=self.height) def others(self, other, name=_other_, up=1): # see .named._namedBase.others '''Check this and an other instance for type compatibility. @arg other: The other instance (any C{type}). @kwarg name: Optional, name for other (C{str}). @kwarg up: Number of call stack frames up (C{int}). @return: The B{C{other}} if compatible. @raise TypeError: Incompatible B{C{other}} C{type}. ''' if not (isinstance(other, self.__class__) or (hasattr(other, _lat_) and hasattr(other, _lon_))): n = _callname(name, classname(self), self.name, up=up + 1) raise _TypeError(name, other, txt=_incompatible(n)) return other @property_RO def philam(self): '''Get the lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). ''' return PhiLam2Tuple(radians(self.lat), radians(self.lon)) @property_RO def philamheight(self): '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.philam.to3Tuple(self.height) def points(self, points, closed=False, base=None): # PYCHOK no cover '''DEPRECATED, use method C{points2}. ''' return points2(points, closed=closed, base=base) def points2(self, points, closed=False, base=None): '''Check a path or polygon represented by points. @arg points: The path or polygon points (C{LatLon}[]) @kwarg closed: Optionally, consider the polygon closed, ignoring any duplicate or closing final B{C{points}} (C{bool}). @kwarg base: Optionally, check all B{C{points}} against this base class, if C{None} don't check. @return: A L{Points2Tuple}C{(number, points)} with the number of points and the points C{list} or C{tuple}. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} are not B{C{base}}. ''' return points2(points, closed=closed, base=base) def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property C{philam}. @return: A L{PhiLam2Tuple}C{(phi, lam)}. ''' return self.philam def toNvector(self, h=None, Nvector=NvectorBase, **Nvector_kwds): '''Convert this point to C{n-vector} (normal to the earth's surface) components, I{including height}. @kwarg h: Optional height, overriding this point's height (C{meter}). @kwarg Nvector: Optional class to return the C{n-vector} components (C{Nvector}) or C{None}. @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if B{C{Nvector=None}}. @return: The C{n-vector} components B{C{Nvector}} or if B{C{Nvector}} is C{None}, a L{Vector4Tuple}C{(x, y, z, h)}. @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. ''' x, y, z = latlon2n_xyz(self.lat, self.lon) r = Vector4Tuple(x, y, z, self.height if h is None else h) if Nvector: r = Nvector(x, y, z, h=r.h, **_xkwds(Nvector_kwds, ll=self)) return _xnamed(r, self.name) def toRepr(self, **kwds): '''This L{LatLon_} as a string "class(<degrees>, ...)". @kwarg kwds: Optional, keyword arguments. @return: Class instance (C{str}). ''' _ = _xkwds_pop(kwds, std=None) # PYCHOK std unused return _item_ps(classname(self), self.toStr(**kwds)) toStr2 = toRepr # PYCHOK for backward compatibility '''DEPRECATED, used method L{LatLon_.toRepr}.''' def toStr(self, form=F_D, prec=6, sep=_COMMA_SPACE_, **kwds): '''This L{LatLon_} as a string "<degrees>, <degrees>". @kwarg form: Optional format, F_D, F_DM, F_DMS for deg°, deg°min′, deg°min′sec″ (C{str}). @kwarg prec: Optional number of decimal digits (0..8 or C{None}). @kwarg sep: Optional separator to join (C{str}). @kwarg kwds: Optional, keyword arguments. @return: Instance (C{str}). ''' t = (latDMS(self.lat, form=form, prec=prec), lonDMS(self.lon, form=form, prec=prec)) if self.height: t += (self.heightStr(),) if self.name: t += (repr(self.name),) if kwds: t += pairs(kwds, prec=prec) return sep.join(t) class _Basequence(_Sequence): # immutable, on purpose '''(INTERNAL) Base class. ''' _array = [] _epsilon = EPS _itemname = _point_ def _contains(self, point): '''(INTERNAL) Check for a matching point. ''' for _ in self._findall(point, ()): return True return False def copy(self, deep=False): '''Make a shallow or deep copy of this instance. @kwarg deep: If C{True} make a deep, otherwise a shallow copy (C{bool}). @return: The copy (C{This class} or subclass thereof). ''' return _xcopy(self, deep=deep) def _count(self, point): '''(INTERNAL) Count the number of matching points. ''' n = 0 for _ in self._findall(point, ()): n += 1 return n @property_doc_(''' the equality tolerance (C{float}).''') def epsilon(self): '''Get the tolerance for equality tests (C{float}). ''' return self._epsilon @epsilon.setter # PYCHOK setter! def epsilon(self, tol): '''Set the tolerance for equality tests. @arg tol: New tolerance (C{scalar}). @raise TypeError: Non-scalar B{C{tol}}. @raise ValueError: Out-of-bounds B{C{tol}}. ''' self._epsilon = Scalar_(tol, name='tolerance') def _find(self, point, start_end): '''(INTERNAL) Find the first matching point index. ''' for i in self._findall(point, start_end): return i return -1 def _findall(self, point, start_end): # PYCHOK no cover '''(INTERNAL) I{Must be implemented/overloaded}. ''' notImplemented(self, self._findall, point, start_end) def _getitem(self, index): '''(INTERNAL) Return point [index] or return a slice. ''' # Luciano Ramalho, "Fluent Python", page 290+, O'Reilly, 2016 if isinstance(index, slice): # XXX an numpy.array slice is a view, not a copy return self.__class__(self._array[index], **self._slicekwds()) else: return self.point(self._array[index]) def _index(self, point, start_end): '''(INTERNAL) Find the first matching point index. ''' for i in self._findall(point, start_end): return i raise _IndexError(self._itemname, point, txt='not found') @property_RO def isNumpy2(self): # PYCHOK no cover '''Is this a Numpy2 wrapper? ''' return False # isinstance(self, (Numpy2LatLon, ...)) @property_RO def isPoints2(self): # PYCHOK no cover '''Is this a LatLon2 wrapper/converter? ''' return False # isinstance(self, (LatLon2psxy, ...)) @property_RO def isTuple2(self): # PYCHOK no cover '''Is this a Tuple2 wrapper? ''' return False # isinstance(self, (Tuple2LatLon, ...)) def _iter(self): '''(INTERNAL) Yield all points. ''' for i in range(len(self)): yield self.point(self._array[i]) def point(self, *attrs): # PYCHOK no cover '''(INTERNAL) I{Must be overloaded}. @arg attrs: Optional arguments. ''' notOverloaded(self, self.point, *attrs) def _range(self, start=None, end=None, step=1): '''(INTERNAL) Return the range. ''' if step > 0: if start is None: start = 0 if end is None: end = len(self) elif step < 0: if start is None: start = len(self) - 1 if end is None: end = -1 else: raise _ValueError(step=step) return range(start, end, step) def _repr(self): '''(INTERNAL) Return a string representation. ''' # XXX use Python 3+ reprlib.repr t = repr(self._array[:1]) # only first row t = '%s ... %s[%s]' % (t[:-1], t[-1:], len(self)) t = ' '.join(t.split()) # coalesce spaces return instr(self, t, **self._slicekwds()) def _reversed(self): # PYCHOK false '''(INTERNAL) Yield all points in reverse order. ''' for i in range(len(self) - 1, -1, -1): yield self.point(self._array[i]) def _rfind(self, point, start_end): '''(INTERNAL) Find the last matching point index. ''' def _r3(start=None, end=None, step=-1): return (start, end, step) # PYCHOK returns for i in self._findall(point, _r3(*start_end)): return i return -1 def _slicekwds(self): # PYCHOK no cover '''(INTERNAL) I{Should be overloaded}. ''' return {} def _zeros(self, *zeros): '''(INTERNAL) Check for near-zero values. ''' return all(abs(z) <= self._epsilon for z in zeros) class _Array2LatLon(_Basequence): # immutable, on purpose '''Base class for Numpy2LatLon or Tuple2LatLon. ''' _array = () _ilat = 0 # row column index _ilon = 0 # row column index _LatLon = LatLon_ # default _shape = () def __init__(self, array, ilat=0, ilon=1, LatLon=None, shape=()): '''Handle a C{NumPy} or C{Tuple} array as a sequence of C{LatLon} points. ''' ais = ('ilat', ilat), ('ilon', ilon) if len(shape) != 2 or shape[0] < 1 or shape[1] < len(ais): raise _IndexError('array.shape', shape) self._array = array self._shape = Shape2Tuple(*shape) # check the point class if LatLon is not None: if isclass(LatLon) and all(hasattr(LatLon, a) for a in LatLon_.__slots__): self._LatLon = LatLon else: raise _IsnotError(_valid_, LatLon=LatLon) # check the attr indices for n, (ai, i) in enumerate(ais): if not isint(i): raise _IsnotError(int.__name__, **{ai: i}) i = int(i) if not 0 <= i < shape[1]: raise _ValueError(ai, i) for aj, j in ais[:n]: if int(j) == i: raise _ValueError(' == '.join(map1(str, ai, aj, i))) setattr(self, _UNDERSCORE_ + ai, i) def __contains__(self, latlon): '''Check for a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @return: C{True} if B{C{latlon}} is present, C{False} otherwise. @raise TypeError: Invalid B{C{latlon}}. ''' return self._contains(latlon) def __getitem__(self, index): '''Return row[index] as C{LatLon} or return a L{Numpy2LatLon} slice. ''' return self._getitem(index) def __iter__(self): '''Yield rows as C{LatLon}. ''' return self._iter() def __len__(self): '''Return the number of rows. ''' return self._shape[0] def __repr__(self): '''Return a string representation. ''' return self._repr() def __reversed__(self): # PYCHOK false '''Yield rows as C{LatLon} in reverse order. ''' return self._reversed() __str__ = __repr__ def count(self, latlon): '''Count the number of rows with a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @return: Count (C{int}). @raise TypeError: Invalid B{C{latlon}}. ''' return self._count(latlon) def find(self, latlon, *start_end): '''Find the first row with a specific lat-/longitude. @arg latlon: Point (C{LatLon}) or 2-tuple (lat, lon). @arg start_end: Optional C{[start[, end]]} index (integers). @return: Index or -1 if not found (C{int}). @raise TypeError: Invalid B{C{latlon}}. ''' return self._find(latlon, start_end) def _findall(self, latlon, start_end): '''(INTERNAL) Yield indices of all matching rows. ''' try: lat, lon = latlon.lat, latlon.lon except AttributeError: try: lat, lon = latlon except (TypeError, ValueError): raise _IsnotError(_valid_, latlon=latlon) for i in self._range(*start_end): row = self._array[i] if self._zeros(row[self._ilat] - lat, row[self._ilon] - lon): yield i def findall(self, latlon, *start_end): '''Yield indices of all rows with a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Indices (C{iterable}). @raise TypeError: Invalid B{C{latlon}}. ''' return self._findall(latlon, start_end) def index(self, latlon, *start_end): # PYCHOK Python 2- issue '''Find index of the first row with a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index (C{int}). @raise IndexError: Point not found. @raise TypeError: Invalid B{C{latlon}}. ''' return self._index(latlon, start_end) @property_RO def ilat(self): '''Get the latitudes column index (C{int}). ''' return self._ilat @property_RO def ilon(self): '''Get the longitudes column index (C{int}). ''' return self._ilon # next = __iter__ def point(self, row): # PYCHOK *attrs '''Instantiate a point C{LatLon}. @arg row: Array row (numpy.array). @return: Point (C{LatLon}). ''' return self._LatLon(row[self._ilat], row[self._ilon]) def rfind(self, latlon, *start_end): '''Find the last row with a specific lat-/longitude. @arg latlon: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(lat, lon)}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @note: Keyword order, first stop, then start. @return: Index or -1 if not found (C{int}). @raise TypeError: Invalid B{C{latlon}}. ''' return self._rfind(latlon, start_end) def _slicekwds(self): '''(INTERNAL) Slice kwds. ''' return dict(ilat=self._ilat, ilon=self._ilon) @property_RO def shape(self): '''Get the shape of the C{NumPy} array or the C{Tuples} as L{Shape2Tuple}C{(nrows, ncols)}. ''' return self._shape def _subset(self, indices): # PYCHOK unused '''(INTERNAL) I{Must be implemented/overloaded}. ''' notImplemented(self, self._subset, indices) def subset(self, indices): '''Return a subset of the C{NumPy} array. @arg indices: Row indices (C{range} or C{int}[]). @note: A C{subset} is different from a C{slice} in 2 ways: (a) the C{subset} is typically specified as a list of (un-)ordered indices and (b) the C{subset} allocates a new, separate C{NumPy} array while a C{slice} is just an other C{view} of the original C{NumPy} array. @return: Sub-array (C{numpy.array}). @raise IndexError: Out-of-range B{C{indices}} value. @raise TypeError: If B{C{indices}} is not a C{range} nor an C{int}[]. ''' if not issequence(indices, tuple): # NO tuple, only list # and range work properly to get Numpy array sub-sets raise _IsnotError(_valid_, indices=type(indices)) n = len(self) for i, v in enumerate(indices): if not isint(v): raise _TypeError(_item_sq(indices=i), v) elif not 0 <= v < n: raise _IndexError(_item_sq(indices=i), v) return self._subset(indices) class LatLon2psxy(_Basequence): '''Wrapper for C{LatLon} points as "on-the-fly" pseudo-xy coordinates. ''' _closed = False _len = 0 _deg2m = None # default, keep degrees _radius = None _wrap = True def __init__(self, latlons, closed=False, radius=None, wrap=True): '''Handle C{LatLon} points as pseudo-xy coordinates. @note: The C{LatLon} latitude is considered the I{pseudo-y} and longitude the I{pseudo-x} coordinate, likewise for L{LatLon2Tuple}. However, 2-tuples C{(x, y)} are considered as I{(longitude, latitude)}. @arg latlons: Points C{list}, C{sequence}, C{set}, C{tuple}, etc. (C{LatLon[]}). @kwarg closed: Optionally, close the polygon (C{bool}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap lat- and longitudes (C{bool}). @raise PointsError: Insufficient number of B{C{latlons}}. @raise TypeError: Some B{C{points}} are not B{C{base}}. ''' self._closed = closed self._len, self._array = points2(latlons, closed=closed) if radius: self._radius = radius self._deg2m = degrees2m(1.0, radius) self._wrap = wrap def __contains__(self, xy): '''Check for a matching point. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @return: C{True} if B{C{xy}} is present, C{False} otherwise. @raise TypeError: Invalid B{C{xy}}. ''' return self._contains(xy) def __getitem__(self, index): '''Return the pseudo-xy or return a L{LatLon2psxy} slice. ''' return self._getitem(index) def __iter__(self): '''Yield all pseudo-xy's. ''' return self._iter() def __len__(self): '''Return the number of pseudo-xy's. ''' return self._len def __repr__(self): '''Return a string representation. ''' return self._repr() def __reversed__(self): # PYCHOK false '''Yield all pseudo-xy's in reverse order. ''' return self._reversed() __str__ = __repr__ def count(self, xy): '''Count the number of matching points. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @return: Count (C{int}). @raise TypeError: Invalid B{C{xy}}. ''' return self._count(xy) def find(self, xy, *start_end): '''Find the first matching point. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index or -1 if not found (C{int}). @raise TypeError: Invalid B{C{xy}}. ''' return self._find(xy, start_end) def _findall(self, xy, start_end): '''(INTERNAL) Yield indices of all matching points. ''' try: x, y = xy.lon, xy.lat def _3xyll(ll): # match LatLon return ll.lon, ll.lat, ll except AttributeError: try: x, y = xy[:2] except (IndexError, TypeError, ValueError): raise _IsnotError(_valid_, xy=xy) def _3xyll(ll): # PYCHOK expected return self.point(ll) for i in self._range(*start_end): xi, yi, _ = _3xyll(self._array[i]) if self._zeros(xi - x, yi - y): yield i def findall(self, xy, *start_end): '''Yield indices of all matching points. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Indices (C{iterator}). @raise TypeError: Invalid B{C{xy}}. ''' return self._findall(xy, start_end) def index(self, xy, *start_end): # PYCHOK Python 2- issue '''Find the first matching point. @arg xy: Point (C{LatLon}) or 2-tuple (x, y) in (C{degrees}). @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index (C{int}). @raise IndexError: Point not found. @raise TypeError: Invalid B{C{xy}}. ''' return self._index(xy, start_end) @property_RO def isPoints2(self): '''Is this a LatLon2 wrapper/converter? ''' return True # isinstance(self, (LatLon2psxy, ...)) # next = __iter__ def point(self, ll): # PYCHOK *attrs '''Create a pseudo-xy. @arg ll: Point (C{LatLon}). @return: An L{Point3Tuple}C{(x, y, ll)}. ''' x, y = ll.lon, ll.lat # note, x, y = lon, lat if self._wrap: x, y = wrap180(x), wrap90(y) if self._deg2m: # convert degrees to meter (or radians) x *= self._deg2m y *= self._deg2m return Point3Tuple(x, y, ll) def rfind(self, xy, *start_end): '''Find the last matching point. @arg xy: Point (C{LatLon}, L{LatLon2Tuple} or 2-tuple C{(x, y)}) in (C{degrees}. @arg start_end: Optional C{[start[, end]]} index (C{int}). @return: Index or -1 if not found (C{int}). @raise TypeError: Invalid B{C{xy}}. ''' return self._rfind(xy, start_end) def _slicekwds(self): '''(INTERNAL) Slice kwds. ''' return dict(closed=self._closed, radius=self._radius, wrap=self._wrap) class NearestOn5Tuple(_NamedTuple): '''5-Tuple C{(lat, lon, distance, angle, height)} all in C{degrees}, except C{height}. The C{distance} is the L{equirectangular_} distance between the closest and the reference B{C{point}} in C{degrees}. The C{angle} from the reference B{C{point}} to the closest point is in compass C{degrees360}, see function L{compassAngle}. The C{height} is the (interpolated) height at the closest point in C{meter} or C{0}. ''' _Names_ = ('lat', 'lon', 'distance', 'angle', 'height') class Numpy2LatLon(_Array2LatLon): # immutable, on purpose '''Wrapper for C{NumPy} arrays as "on-the-fly" C{LatLon} points. ''' def __init__(self, array, ilat=0, ilon=1, LatLon=None): '''Handle a C{NumPy} array as a sequence of C{LatLon} points. @arg array: C{NumPy} array (C{numpy.array}). @kwarg ilat: Optional index of the latitudes column (C{int}). @kwarg ilon: Optional index of the longitudes column (C{int}). @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}). @raise IndexError: If B{C{array.shape}} is not (1+, 2+). @raise TypeError: If B{C{array}} is not a C{NumPy} array or C{LatLon} is not a class with C{lat} and C{lon} attributes. @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values are the same or out of range. @example: >>> type(array) <type 'numpy.ndarray'> # <class ...> in Python 3+ >>> points = Numpy2LatLon(array, lat=0, lon=1) >>> simply = simplifyRDP(points, ...) >>> type(simply) <type 'numpy.ndarray'> # <class ...> in Python 3+ >>> sliced = points[1:-1] >>> type(sliced) <class '...Numpy2LatLon'> ''' try: # get shape and check some other numpy.array attrs s, _, _ = array.shape, array.nbytes, array.ndim # PYCHOK expected except AttributeError: raise _IsnotError('NumPy', array=type(array)) _Array2LatLon.__init__(self, array, ilat=ilat, ilon=ilon, LatLon=LatLon, shape=s) @property_RO def isNumpy2(self): '''Is this a Numpy2 wrapper? ''' return True # isinstance(self, (Numpy2LatLon, ...)) def _subset(self, indices): return self._array[indices] # NumPy special class Point3Tuple(_NamedTuple): '''3-Tuple C{(x, y, ll)} in C{meter}, C{meter} and C{LatLon}. ''' _Names_ = (_x_, _y_, 'll') class Shape2Tuple(_NamedTuple): '''2-Tuple C{(nrows, ncols)}, the number of rows and columns, both C{int}. ''' _Names_ = ('nrows', 'ncols') class Tuple2LatLon(_Array2LatLon): '''Wrapper for tuple sequences as "on-the-fly" C{LatLon} points. ''' def __init__(self, tuples, ilat=0, ilon=1, LatLon=None): '''Handle a list of tuples, each containing a lat- and longitude and perhaps other values as a sequence of C{LatLon} points. @arg tuples: The C{list}, C{tuple} or C{sequence} of tuples (C{tuple}[]). @kwarg ilat: Optional index of the latitudes value (C{int}). @kwarg ilon: Optional index of the longitudes value (C{int}). @kwarg LatLon: Optional C{LatLon} class to use (L{LatLon_}). @raise IndexError: If I{(len(B{C{tuples}}), min(len(t) for t in B{C{tuples}}))} is not (1+, 2+). @raise TypeError: If B{C{tuples}} is not a C{list}, C{tuple} or C{sequence} or if B{C{LatLon}} is not a C{LatLon} with C{lat}, C{lon} and C{name} attributes. @raise ValueError: If the B{C{ilat}} and/or B{C{ilon}} values are the same or out of range. @example: >>> tuples = [(0, 1), (2, 3), (4, 5)] >>> type(tuples) <type 'list'> # <class ...> in Python 3+ >>> points = Tuple2LatLon(tuples, lat=0, lon=1) >>> simply = simplifyRW(points, 0.5, ...) >>> type(simply) <type 'list'> # <class ...> in Python 3+ >>> simply [(0, 1), (4, 5)] >>> sliced = points[1:-1] >>> type(sliced) <class '...Tuple2LatLon'> >>> sliced ...Tuple2LatLon([(2, 3), ...][1], ilat=0, ilon=1) >>> closest, _ = nearestOn2(LatLon_(2, 1), points, adjust=False) >>> closest LatLon_(lat=1.0, lon=2.0) >>> closest, _ = nearestOn2(LatLon_(3, 2), points) >>> closest LatLon_(lat=2.001162, lon=3.001162) ''' _xinstanceof(list, tuple, tuples=tuples) s = len(tuples), min(len(_) for _ in tuples) _Array2LatLon.__init__(self, tuples, ilat=ilat, ilon=ilon, LatLon=LatLon, shape=s) @property_RO def isTuple2(self): '''Is this a Tuple2 wrapper? ''' return True # isinstance(self, (Tuple2LatLon, ...)) def _subset(self, indices): return type(self._array)(self._array[i] for i in indices) def _area2(points, adjust, wrap): # return the signed area in radians squared # setting radius=1 converts degrees to radians pts = LatLon2psxy(points, closed=True, radius=1, wrap=wrap) def _rads2(n, pts): # trapezoidal areas in rads**2 x1, y1, _ = pts[n-1] for i in range(n): x2, y2, _ = pts[i] w, x2 = unrollPI(x1, x2, wrap=wrap if i < (n - 1) else False) # approximate trapezoid by a rectangle, adjusting # the top width by the cosine of the latitudinal # average and bottom width by some fudge factor h = (y2 + y1) * 0.5 if adjust: c = cos(h) if abs(h) < PI_2 else 0 w *= (c + 1.2876) * 0.5 yield h * w # signed trapezoidal area x1, y1 = x2, y2 return fsum(_rads2(len(pts), pts)), pts def _areaError(pts, near_=NN): # imported by .ellipsoidalKarney '''(INTERNAL) Area issue. ''' return _ValueError(near_ + 'zero or polar area', txt='%s ...' % (pts[:3],)) def areaOf(points, adjust=True, radius=R_M, wrap=True): '''Approximate the area of a polygon. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: Approximate area (C{meter}, same units as B{C{radius}}, I{squared}). @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{radius}}. @note: This area approximation has limited accuracy and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. @see: L{sphericalNvector.areaOf}, L{sphericalTrigonometry.areaOf} and L{ellipsoidalKarney.areaOf}. ''' a, _ = _area2(points, adjust, wrap) return abs(a) * Radius(radius)**2 def boundsOf(points, wrap=True, LatLon=None): '''Determine the lower-left SW and upper-right NE corners of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat- and longitudes (C{bool}). @kwarg LatLon: Optional class to return the C{bounds} corners (C{LatLon}) or C{None}. @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)} as B{C{LatLon}}s if B{C{LatLon}} is C{None} a L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @example: >>> b = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) >>> boundsOf(b) # False >>> 45.0, 1.0, 46.0, 2.0 ''' pts = LatLon2psxy(points, closed=False, radius=None, wrap=wrap) lox, loy, _ = hix, hiy, _ = pts[0] for x, y, _ in pts: # [1:] if lox > x: lox = x elif hix < x: hix = x if loy > y: loy = y elif hiy < y: hiy = y r = Bounds4Tuple(loy, lox, hiy, hix) if LatLon is None else \ Bounds2Tuple(LatLon(loy, lox), LatLon(hiy, hix)) # PYCHOK inconsistent return r def centroidOf(points, wrap=True, LatLon=None): '''Determine the centroid of a polygon. @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @kwarg LatLon: Optional class to return the centroid (L{LatLon}) or C{None}. @return: Centroid location (B{C{LatLon}}) or a L{LatLon2Tuple}C{(lat, lon)} if B{C{LatLon}} is C{None}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: The B{C{points}} enclose a pole or near-zero area. @see: U{Centroid<https://WikiPedia.org/wiki/Centroid#Of_a_polygon>} and U{Calculating The Area And Centroid Of A Polygon <https://www.Seas.UPenn.edu/~sys502/extra_materials/ Polygon%20Area%20and%20Centroid.pdf>}. ''' # setting radius=1 converts degrees to radians pts = LatLon2psxy(points, closed=True, radius=1, wrap=wrap) n = len(pts) A, X, Y = Fsum(), Fsum(), Fsum() x1, y1, _ = pts[n-1] for i in range(n): x2, y2, _ = pts[i] if wrap and i < (n - 1): _, x2 = unrollPI(x1, x2, wrap=True) t = x1 * y2 - x2 * y1 A += t X += t * (x1 + x2) Y += t * (y1 + y2) # XXX more elaborately: # t1, t2 = x1 * y2, -(x2 * y1) # A.fadd_(t1, t2) # X.fadd_(t1 * x1, t1 * x2, t2 * x1, t2 * x2) # Y.fadd_(t1 * y1, t1 * y2, t2 * y1, t2 * y2) x1, y1 = x2, y2 A = A.fsum() * 3.0 # 6.0 / 2.0 if abs(A) < EPS: raise _areaError(points, near_='near-') Y, X = degrees90(Y.fsum() / A), degrees180(X.fsum() / A) return LatLon2Tuple(Y, X) if LatLon is None else LatLon(Y, X) def _imdex2(closed, n): # imported by sphericalNvector, -Trigonometry '''(INTERNAL) Return first and second index. ''' return (n-1, 0) if closed else (0, 1) def isclockwise(points, adjust=False, wrap=True): '''Determine the direction of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{points}} are clockwise, C{False} otherwise. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: The B{C{points}} enclose a pole or zero area. @example: >>> f = LatLon(45,1), LatLon(45,2), LatLon(46,2), LatLon(46,1) >>> isclockwise(f) # False >>> isclockwise(reversed(f)) # True ''' a, _ = _area2(points, adjust, wrap) if a > 0: return True elif a < 0: return False # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> raise _areaError(points) def isconvex(points, adjust=False, wrap=True): '''Determine whether a polygon is convex. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{points}} are convex, C{False} otherwise. @raise CrossError: Some B{C{points}} are colinear. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @example: >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) >>> isconvex(t) # True >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) >>> isconvex(f) # False ''' return bool(isconvex_(points, adjust=adjust, wrap=wrap)) def isconvex_(points, adjust=False, wrap=True): '''Determine whether a polygon is convex and clockwise. @arg points: The polygon points (C{LatLon}[]). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{+1} if B{C{points}} are convex clockwise, C{-1} for convex counter-clockwise B{C{points}}, C{0} otherwise. @raise CrossError: Some B{C{points}} are colinear. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @example: >>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2) >>> isconvex_(t) # +1 >>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1) >>> isconvex_(f) # 0 ''' def _unroll_adjust(x1, y1, x2, y2, wrap): x21, x2 = unroll180(x1, x2, wrap=wrap) if adjust: y = radians(y1 + y2) * 0.5 x21 *= cos(y) if abs(y) < PI_2 else 0 return x21, x2 pts = LatLon2psxy(points, closed=True, radius=None, wrap=wrap) c, n, s = crosserrors(), len(pts), 0 x1, y1, _ = pts[n-2] x2, y2, _ = pts[n-1] x21, x2 = _unroll_adjust(x1, y1, x2, y2, False) for i in range(n): x3, y3, ll = pts[i] x32, x3 = _unroll_adjust(x2, y2, x3, y3, wrap if i < (n - 2) else False) # get the sign of the distance from point # x3, y3 to the line from x1, y1 to x2, y2 # <https://WikiPedia.org/wiki/Distance_from_a_point_to_a_line> s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2) if s3 > 0: # x3, y3 on the right if s < 0: # non-convex return 0 s = +1 elif s3 < 0: # x3, y3 on the left if s > 0: # non-convex return 0 s = -1 elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0: # colinear u-turn: x3, y3 not on the # opposite side of x2, y2 as x1, y1 raise CrossError(points=ll, txt='colinear') x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32 return s # all points on the same side def isenclosedBy(point, points, wrap=False): # MCCABE 15 '''Determine whether a point is enclosed by a polygon. @arg point: The point (C{LatLon} or 2-tuple C{(lat, lon)}). @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{point}} is inside the polygon, C{False} otherwise. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{point}}, lat- or longitude. @see: L{sphericalNvector.LatLon.isenclosedBy}, L{sphericalTrigonometry.LatLon.isenclosedBy} and U{MultiDop GeogContainPt<https://GitHub.com/NASA/MultiDop>} (U{Shapiro et al. 2009, JTECH <https://Journals.AMetSoc.org/doi/abs/10.1175/2009JTECHA1256.1>} and U{Potvin et al. 2012, JTECH <https://Journals.AMetSoc.org/doi/abs/10.1175/JTECH-D-11-00019.1>}). ''' try: y0, x0 = point.lat, point.lon except AttributeError: try: y0, x0 = map1(float, *point[:2]) except (IndexError, TypeError, ValueError) as x: raise _ValueError(point=point, txt=str(x)) pts = LatLon2psxy(points, closed=True, radius=None, wrap=wrap) n = len(pts) if wrap: x0, y0 = wrap180(x0), wrap90(y0) def _dxy(x1, i): x2, y2, _ = pts[i] dx, x2 = unroll180(x1, x2, wrap=i < (n - 1)) return dx, x2, y2 else: x0 = fmod(x0, 360.0) # not x0 % 360 def _dxy(x1, i): # PYCHOK expected x, y, _ = pts[i] x %= 360.0 if x < (x0 - 180): x += 360 elif x >= (x0 + 180): x -= 360 return (x - x1), x, y e = m = False s = Fsum() _, x1, y1 = _dxy(x0, n - 1) for i in range(n): dx, x2, y2 = _dxy(x1, i) # ignore duplicate and near-duplicate pts if max(abs(dx), abs(y2 - y1)) > EPS: # determine if polygon edge (x1, y1)..(x2, y2) straddles # point (lat, lon) or is on boundary, but do not count # edges on boundary as more than one crossing if abs(dx) < 180 and (x1 < x0 <= x2 or x2 < x0 <= x1): m = not m dy = (x0 - x1) * (y2 - y1) - (y0 - y1) * dx if (dy > 0 and dx >= 0) or (dy < 0 and dx <= 0): e = not e s.fadd_(sin(radians(y2))) x1, y1 = x2, y2 # An odd number of meridian crossings means, the polygon # contains a pole. Assume it is the pole on the hemisphere # containing the polygon mean point and if the polygon does # contain the North Pole, flip the result. if m and s.fsum() > 0: e = not e return e def ispolar(points, wrap=False): '''Check whether a polygon encloses a pole. @arg points: The polygon points (C{LatLon}[]). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: C{True} if the polygon encloses a pole, C{False} otherwise. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon} or don't have C{bearingTo2}, C{initialBearingTo} and C{finalBearingTo} methods. ''' n, points = points2(points, closed=True) def _cds(n, points): # iterate over course deltas p1 = points[n-1] try: # LatLon must have initial- and finalBearingTo b1, _ = p1.bearingTo2(points[0], wrap=wrap) except AttributeError: raise _IsnotError('.bearingTo2', points=p1) for i in range(n): p2 = points[i] if not p2.isequalTo(p1, EPS): b, b2 = p1.bearingTo2(p2, wrap=wrap) yield wrap180(b - b1) # (b - b1 + 540) % 360 - 180 yield wrap180(b2 - b) # (b2 - b + 540) % 360 - 180 p1, b1 = p2, b2 # sum of course deltas around pole is 0° rather than normally ±360° # <https://blog.Element84.com/determining-if-a-spherical-polygon-contains-a-pole.html> s = fsum(_cds(n, points)) # XXX fix (intermittant) edge crossing pole - eg (85,90), (85,0), (85,-90) return abs(s) < 90 # "zero-ish" def nearestOn5(point, points, closed=False, wrap=False, LatLon=None, **options): '''Locate the point on a path or polygon closest to an other point. If the given point is within the extent of a polygon edge, the closest point is on that edge, otherwise the closest point is the nearest of that edge's end points. Distances are approximated by function L{equirectangular_}, subject to the supplied B{C{options}}. @arg point: The other, reference point (C{LatLon}). @arg points: The path or polygon points (C{LatLon}[]). @kwarg closed: Optionally, close the path or polygon (C{bool}). @kwarg wrap: Wrap and L{unroll180} longitudes and longitudinal delta (C{bool}) in function L{equirectangular_}. @kwarg LatLon: Optional class to return the closest point (L{LatLon}) or C{None}. @kwarg options: Other keyword arguments for function L{equirectangular_}. @return: A L{NearestOn3Tuple}C{(closest, distance, angle)} with the {closest} point (B{C{LatLon}}) or if B{C{LatLon}} is C{None} a L{NearestOn5Tuple}C{(lat, lon, distance, angle, height)}. The C{distance} is the L{equirectangular_} distance between the C{closest} and reference B{C{point}} in C{degrees}. The C{angle} from the reference B{C{point}} to the C{closest} is in compass C{degrees360}, like function L{compassAngle}. @raise LimitError: Lat- and/or longitudinal delta exceeds the B{C{limit}}, see function L{equirectangular_}. @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @see: Function L{degrees2m} to convert C{degrees} to C{meter}. ''' n, points = points2(points, closed=closed) def _d2yx(p2, p1, u, i): w = wrap if (not closed or i < (n - 1)) else False # equirectangular_ returns a Distance4Tuple(distance # in degrees squared, delta lat, delta lon, p2.lon # unroll/wrap); the previous p2.lon unroll/wrap # is also applied to the next edge's p1.lon return equirectangular_(p1.lat, p1.lon + u, p2.lat, p2.lon, wrap=w, **options) def _h(p): try: # get height return p.height or 0 except AttributeError: return 0 # point (x, y) on axis rotated ccw by angle a: # x' = y * sin(a) + x * cos(a) # y' = y * cos(a) - x * sin(a) # # distance (w) along and perpendicular (h) to # a line thru point (dx, dy) and the origin: # w = (y * dy + x * dx) / hypot(dx, dy) # h = (y * dx - x * dy) / hypot(dx, dy) # # closest point on that line thru (dx, dy): # xc = dx * w / hypot(dx, dy) # yc = dy * w / hypot(dx, dy) # or # xc = dx * f # yc = dy * f # with # f = w / hypot(dx, dy) # or # f = (y * dy + x * dx) / hypot2(dx, dy) i, m = _imdex2(closed, n) p2 = c = points[i] u2 = u = 0 d, dy, dx, _ = _d2yx(p2, point, u2, i) for i in range(m, n): p1, u1, p2 = p2, u2, points[i] # iff wrapped, unroll lon1 (actually previous # lon2) like function unroll180/-PI would've d21, y21, x21, u2 = _d2yx(p2, p1, u1, i) if d21 > EPS: # distance point to p1, y01 and x01 inverted d2, y01, x01, _ = _d2yx(point, p1, u1, n) if d2 > EPS: w2 = y01 * y21 + x01 * x21 if w2 > 0: if w2 < d21: # closest is between p1 and p2, use # original delta's, not y21 and x21 f = w2 / d21 p1 = LatLon_(favg(p1.lat, p2.lat, f=f), favg(p1.lon, p2.lon + u2, f=f), height=favg(_h(p1), _h(p2), f=f)) u1 = 0 else: # p2 is closest p1, u1 = p2, u2 d2, y01, x01, _ = _d2yx(point, p1, u1, n) if d2 < d: # p1 is closer, y01 and x01 inverted c, u, d, dy, dx = p1, u1, d2, -y01, -x01 d, a, h = hypot(dx, dy), degrees360(atan2(dx, dy)), _h(c) if LatLon is None: r = NearestOn5Tuple(c.lat, c.lon + u, d, a, h) else: r = LatLon(c.lat, c.lon + u, height=h) r = NearestOn3Tuple(r, d, a) return _xnamed(r, nameof(point)) def perimeterOf(points, closed=False, adjust=True, radius=R_M, wrap=True): '''Approximate the perimeter of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg closed: Optionally, close the path or polygon (C{bool}). @kwarg adjust: Adjust the wrapped, unrolled longitudinal delta by the cosine of the mean latitude (C{bool}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). @return: Approximate perimeter (C{meter}, same units as B{C{radius}}). @raise PointsError: Insufficient number of B{C{points}} @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: Invalid B{C{radius}}. @note: This perimeter is based on the L{equirectangular_} distance approximation and is ill-suited for regions exceeding several hundred Km or Miles or with near-polar latitudes. @see: L{sphericalTrigonometry.perimeterOf} and L{ellipsoidalKarney.perimeterOf}. ''' pts = LatLon2psxy(points, closed=closed, radius=None, wrap=False) def _degs(n, pts, closed): # angular edge lengths in degrees i, m = _imdex2(closed, n) x1, y1, _ = pts[i] u = 0 # previous x2's unroll/wrap for i in range(m, n): x2, y2, _ = pts[i] w = wrap if (not closed or i < (n - 1)) else False # apply previous x2's unroll/wrap to new x1 _, dy, dx, u = equirectangular_(y1, x1 + u, y2, x2, adjust=adjust, limit=None, wrap=w) yield hypot(dx, dy) x1, y1 = x2, y2 d = fsum(_degs(len(pts), pts, closed)) return degrees2m(d, radius=radius) __all__ += _ALL_DOCS(NearestOn5Tuple, Point3Tuple, Shape2Tuple) # **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.